Hardy–Orlicz Spaces of Dirichlet Series: An Interpolation Problem on Abscissae of Convergence. (5th November 2019) - Bailleul, Maxime; Lefèvre, Pascal; Rodríguez-Piazza, Luis
Abstract: The study of Hardy spaces of Dirichlet series denoted by H^p (p≥ 1 ) was initiated in [7 ] when p=2 and p=∞ , and in [2 ] for the general case. In this paper we introduce the Orlicz version of spaces of Dirichlet series H^ψ . We focus on the case ψ =ψ _q(t)=(t^q)-1, and we compute the abscissa of convergence for these spaces. It turns out that its value is {1/q , 1/2} filling the gap between the case H^∞ , where the abscissa is equal to 0, and the case H^p for p finite, where the abscissa is equal to 1/2 . The upper-bound estimate relies on an elementary method that applies to many spaces of Dirichlet series. This answers a question raised by Hedenmalm in [6 ].